 Solution

ID: past-exam-of-the-options-ii-course-of-the-university-of-oxford/2013/d4/d/i/solution

Exactly those integrable functions that vanish almost everywhere:

∥ f ∥_{1} = 0 ⟺ f = 0 almost everywhere .

Thus this expression is a seminorm on actual functions, becoming a norm after the quotient in part (ii).

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